Your channel is so perfect. Actualy even the robotic way you present the facts fits. This shoudn't be the only source, but I think every student of General Relativity should know about your channel. I would be happy if you would make more about QFT too. Greetings from Berlin
@eigenchris
2 жыл бұрын
Thanks. Unfortunately QFT is still pretty mysterious to me, so I won't be able to make videos anytime soon. I do plan on making videos on spinors in 2022, though, which might help out people learning QFT.
@Leon-yl7jx
2 жыл бұрын
Pls make it fast, it´s probably going to help me.
@ProfessorBeautiful
Жыл бұрын
The channel viascience might interest you, @Leon. It leads from beginnings all the way up to QFT and peeks across into it (creation and destruction operators, at least), with the serious attention to detail that we love about the work that eigenchris has done.
@oriaw9525
2 жыл бұрын
Precession calculation: you could integrate d phi = du / sqrt( ...u... ) from aphelion to perihelion, double it, subtract 2pi, and done. Solving a first order DE by turning it into second order is something I feel too involved, though your explanation is far better than similar ones I've seen on the net.
@lourencoentrudo
2 жыл бұрын
Man your videos just keep getting better and better. A few questions tho! Does the energy of a given spacetime always depend on solely on g_tt like this E/m one, or was it just a coincidence? Additionally, would you consider talking about GR Lagrangian/ action/hamiltonian in this series? I think it would add greatly to understanding how energy is defined in GR.
@eigenchris
2 жыл бұрын
I think the answer to that question depends on "Killing vectors", and I'm being a bit vague about those because I haven't properly studied them yet. My understanding is that a Killing vector field indicates a symmetry of your spacetime. So in Schwarzschild spacetime, e_t is a Killing vector because the spacetime has "translation symmetry along the ct coordinate". e_phi is also a killing vector field because the spacetime has "translation symmetry along the phi coordinate". Every killing vector field will give us a conserved quantity. In the case of e_t, the conserved quantity is the energy I showed. In the case of e_phi, the conserved quantity is angular momentum. If your spacetime has no symmetries, I think you just don't end up with conserved quantities. Killing vectors are determined by "Killing's equation", and I think it just happens to be the case that the conserved quantity of the e_t killing vector field gives a conserved quantity involving g_tt. I may make a video on this eventually, but probably not for a few months. Alex Flournoy has a video on this you might try watching: kzitem.info/news/bejne/sqacrqxokoWJZXY . As for the Lagriangian stuff on GR, that's a possibility, but it's at the bottom of my priority list. I feel I don't understand Lagrangians very well and I likely can't explain it properly right now.
@Astro-X
Жыл бұрын
For the Sun-Earth system, where are the 2 stable and unstable circular orbits? Could the Earth orbit the Sun at a different radius other than these 2 points??
@WildGamez
2 жыл бұрын
Omg I can finally appreciate einsteins thoughts
@tomjoyce9401
Жыл бұрын
The Relativity/Tensor series is by far the most effective pedagogical presentation of GR that I have seen in any books or videos, and I have reviewed quite a few. I especially enjoyed the time you devoted to working through the perihelion math. Truly excellent!
@caseyglick5957
2 жыл бұрын
One of the great parts of the story of Mercury's perihelion shift was that the shift had been known since the mid-1800s, and was assumed to be a result of an innermost planet named Vulcan. Urbain Le Verrier, the French scientist who discovered Neptune by a Newtonian perturbation analysis on the orbit of Uranus, spent his entire life looking for Vulcan. At the time Einstein published his proof, there were still people looking for it, even though it had never managed to show up where people had predicted it'd be (despite multiple observation attempts during eclipses.) I'd highly recommend checking out "The Hunt for Vulcan"
@danvieira6263
2 жыл бұрын
It's taken me around 3 months but I've finally caught up every single one of your videos right from the Beginning of Tensors to these very applications of the Schwarzschild Metric. This is such an utterly invaluable KZitem channel. I've never come across a more detailed educational series, even going the extra mile to be totally in-tune with the viewer and provide extra detail at moments when necessary. The clarity you provide and ability to convey the physicality behind the abstract math is so appreciated. Can't believe I'm finally at a point of being able to somewhat intuit the concepts of GR thanks to the solid mathematical foundation you've provided literally for free. Sorry for this essay but you're a true legend eigenchris - just had to show my appreciation! Can't wait to pick up an actual textbook and try my own hand at some problems now, but more importantly can't wait for your future vids!
@eigenchris
2 жыл бұрын
I'm happy this has helped you along your way to understanding GR. It took me a long time to understand all this, so my hope is that it makes it easier for others who watch.
@babai08_
Жыл бұрын
Hi, you said that curly E is energy/mass, but then showed it was P^t, which is E/c, so is curly E actually E/mc?
@FermionPhysics
2 жыл бұрын
Very interesting video. I will use some of these concepts in my own lectures. You have a nice presentation style
@JakobWierzbowski
2 жыл бұрын
Hopefully you show him some gratitude by buying him a Kofi :-)
@eigenchris
2 жыл бұрын
Thanks!
@eigenchris
2 жыл бұрын
Tips aren't really needed. People can enjoy the videos free if they want.
@frankdimeglio8216
2 жыл бұрын
@@eigenchris UNDERSTANDING TIME (AND TIME DILATION) PURSUANT TO THE BALANCED, THEORETICAL, AND CLEAR MATHEMATICAL PROOF THAT E=MC2 IS F=MA (OF NECESSITY): Stellar clustering ALSO proves ON BALANCE that ELECTROMAGNETISM/energy is gravity, AS E=MC2 is CLEARLY F=ma ON BALANCE. Gravity is ELECTROMAGNETISM/energy, AS E=MC2 is clearly F=ma IN BALANCE !!! This explains the fourth dimension AND the term c4 (from Einstein's field equations). Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=MC2 IS F=ma ON BALANCE; AS the stars AND PLANETS are POINTS in the night sky. GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS E=MC2 IS F=ma ON BALANCE; AS ELECTROMAGNETISM/energy is gravity. TIME dilation ULTIMATELY proves ON BALANCE that E=MC2 IS F=ma IN BALANCE, AS ELECTROMAGNETISM/energy is gravity; AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE. Accordingly, the rotation of WHAT IS THE MOON matches it's revolution. The stars AND PLANETS are POINTS in the night sky. So, it makes perfect sense that the planets will move away from WHAT IS THE SUN very, very, very SLIGHTLY. Carefully consider what is THE EYE ON BALANCE !!! (Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black.) E=MC2 is CLEARLY proven to be F=ma ON BALANCE. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/energy is gravity. (Gravity is ELECTROMAGNETISM/energy ON BALANCE, AS E=MC2 IS clearly F=ma IN BALANCE.) Carefully consider what is the speed of light (c). A PHOTON may be placed at the center of what is THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light (c); AS ELECTROMAGNETISM/energy is gravity; AS E=MC2 IS clearly F=ma ON BALANCE. The stars AND PLANETS are POINTS in the night sky !!! Indeed, TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=MC2 is CLEARLY F=ma ON BALANCE; AS ELECTROMAGNETISM/energy is gravity. Carefully consider what is THE EARTH/ground AND what is THE EYE ON BALANCE !!! The sky is BLUE, AND THE EARTH is ALSO BLUE. THE EARTH is a BALANCED MIDDLE DISTANCE form in relation to the speed of light (c) AND what is THE SUN (AS what is a linked AND BALANCED opposite) pursuant to the universal (and CLEAR) fact that E=MC2 IS F=ma ON BALANCE, AS ELECTROMAGNETISM/energy is gravity. The stars AND PLANETS are POINTS in the night sky. Gravity is ELECTROMAGNETISM/energy. E=MC2 IS clearly proven to be F=ma ON BALANCE. Carefully consider what is THE EARTH/ground !!! Great. "Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS E=MC2 IS F=ma IN BALANCE; AS ELECTROMAGNETISM/energy is gravity. Accordingly, objects (AND WHAT IS the falling MAN) fall at the SAME RATE (neglecting air resistance, of course); AS ELECTROMAGNETISM/energy is gravity; AS E=MC2 is CLEARLY proven to be F=ma ON BALANCE. Gravity is clearly ELECTROMAGNETISM/energy, AS E=MC2 is clearly F=ma IN BALANCE !!! It all CLEARLY makes perfect sense, AS BALANCE AND completeness go hand in hand. Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=MC2 is clearly F=ma ON BALANCE; AS ELECTROMAGNETISM/energy is gravity. E=MC2 is CLEARLY F=ma ON BALANCE. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/energy is gravity. Gravity is ELECTROMAGNETISM/energy ON BALANCE !!! (Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE. BALANCED inertia/INERTIAL RESISTANCE is fundamental.) I have mathematically unified physics/physical experience, AS E=MC2 is CLEARLY F=ma ON BALANCE !!! GREAT !!! ELECTROMAGNETISM/energy is gravity !!! By Frank DiMeglio
@alphabeta7275
2 жыл бұрын
Another fine addition to our understanding from a modest and gifted educator. Thank you Eigenchris.
@kimchi_taco
4 ай бұрын
I feel like your voice is voice of god 🙏
@MasterHigure
Жыл бұрын
Something has been bothering me. Einstein demonstrated how GR predicted the correct precession of Mercury's orbit in 1915, but Schwarzschild only published his metric in 1916. How did Einstein do it?
@ritemolawbks8012
Жыл бұрын
If you're still interested in how Einstein had approximated and calculated the precession of perihelion without a solving the field equations and before the _Schwarzschild_ _Solution,_ Sean Carroll's online lecture series, *The* *Biggest* *Ideas* *in* *the* *Universe,* describes it. Below is the link to the video on gravity and an introduction to the mathematics of _general_ relativity. kzitem.info/news/bejne/lGtp0nl4b2WarJw
@MasterHigure
Жыл бұрын
@@ritemolawbks8012 Awesome! I'll take a look when I have some time.
@DrBrianKeating
3 ай бұрын
Awesome content even for my graduate students Thanks
@criticalthinking575
2 жыл бұрын
The best channel for tensors.. Really.. I was struggling a lot with them initially.... But yours channel was the one which really helped me to learn those
@narfwhals7843
2 жыл бұрын
How did Einstein calculate the perihelion shift without knowing the metric? This was his main selling point for GR (in addition to reproducing newtonian gravity) in his original paper but at that point he still assumed his equations were actually not solvable as far as I know. He also calculated the bending of light to be twice the value of what newtonian gravity could account for before anyone ever solved his equations. What actually is responsible for this additional factor of 2? I always just assumed that it was sort of what the equivalence principle gives you plus the effect of space curvature for a distant observer but that's really just a guess.
@eigenchris
2 жыл бұрын
I don't understand his full procedure, but you can check out Einstein's original papers at einsteinpapers.press.princeton.edu/vol6-trans/ . In particular, you can look at Doc 24: "Explanation of the perihelion motion of mercury from the general theory of relativity". He makes many of the same assumptions you'd see in the Schwarzschild metric, and even comes to the conclusion that g_tt has the form "(1 - a/r)" where "a" is a constant. To be honest I find a lot of these papers hard to comprehend, but you'll see some formulas that look close to the ones in this video. Also, be warned that in some of the earlier papers, Einstein goes down the wrong track at some points (for example, he seems to think the metric determinant should be -1 in some of his early GR papers; no idea why).
@eigenchris
2 жыл бұрын
As for the "factor of 2" thing, I'm not really sure about that yet.
@narfwhals7843
2 жыл бұрын
@@eigenchris Thank you for the reply! I think some of the difficulty in comprehending Einstein's papers comes from his use of language plus the translation. They are already difficult to read in German, as well. He also handwaves a lot on some occasions, thinking things should be obvious, and I'm not really convinced he was "fluent" in tensor calculus by the time he first published GR. He had had a lot of help with the math that describe his ideas (from Grossmann and I believe Levi-Civita as well) and I think he got more rigorous later on(after people like Friednmann corrected him). It is somewhat comforting, though, to know that he was only human.
@mrmilionphysics8342
2 жыл бұрын
Keep going ❤️
@dottormaelstrom
2 жыл бұрын
Imma comment this under every video until you answer me. Dude, it's 2 AM, I'd really like to watch this but my eyes are bleeding. Could you please use a dark color scheme (white text on black background)? Thank you, all the best.
@GeorgeCl00n3y
2 жыл бұрын
You could also watch this in daylight. But I get what you mean.
@CallOFDutyMVP666
2 жыл бұрын
Your sleep schedule needs a perihelion shift
@eigenchris
2 жыл бұрын
I'll try it out before the end of the year and see if people like it or not.
@dottormaelstrom
2 жыл бұрын
@@eigenchris T H A N K Y O U
@luudest
Жыл бұрын
Interestingly, Einstein did compute Mercury's perihelion shift (1915) before the Schwarzschild Metric was derived (1916)
@avinashsparrow2911
2 жыл бұрын
SIR I HAVE A QUESTION FOR U ...🤡🤡🤡🤡WHAT INSTEAD OF FORMULATING SPECIAL THEORY OF RELATIVITY BY TAKING LIGHT WAVE 🚈💡 ON MOVING TRAIN ...WE TAKE GRAVITATIONAL wave 🌊 PRODUCED BY IT AND IF space contracts then what happens to gravitational waves ...since acc. To GTR gravitation is curvature in space time
@pacolibre5411
8 ай бұрын
Well, well, well, physicists. Who’s making small angle approximations now?!
@chritophergaafele8922
Ай бұрын
Its funny because when one of Eddington's students proposed the exitance of black holes born due to death of stars, he(Eddington) used to dismiss it as nonsense
@greenguo1424
5 ай бұрын
32:02, I think the final line on the slide should have the term 4𝑏 sin2𝜙, not 2𝑏 sin2𝜙
@officiallyaninja
2 ай бұрын
5:26 typo: says uncharnged instead of uncharged
@riadhalrabeh3783
2 жыл бұрын
It is wrong to say that lensing and the bending of light are beyond Newton's gravity. The deflection of a projectile in Newton's gravity is a function of the speed of the projectile and the mass of the bending object and NOT a function of the projectile mass.. thus the laws apply to massless as well as massive projectiles.. this is how Newton derived his star light deflection by the sun.. hence lensing is Newtonian too. The factor of 2 between Einstein and Newton results is not an error. It comes from the symmetry of the projectile path before and after the encounter. Newton calculated only one half path deflection.
@amateurkim5619
Жыл бұрын
14:10 Energy Expression (This is my bookmark. Sorry!)
@mariobriccetti6462
11 ай бұрын
Wow, great videos but at 5:28 uncharnged is not uncharged.
@lowersaxon
Жыл бұрын
Q: Did A.E. all these calculations in 1919?
@matthias7335
Жыл бұрын
Thanks for these videos, they are very helpful indeed. Minor observation: On 33:45 there seems to be a typo (minus sign instead of equal sign).
@eigenchris
Жыл бұрын
Yeah, my bad.
@petergreen5337
Ай бұрын
❤Thanks very much.
@allykid4720
2 жыл бұрын
9:47. Units of E^2/m vs mc^2 don't match?
@eigenchris
2 жыл бұрын
Yeah, the left hand side should really be E/c if you take E to have units of Joules.
@mithsaragame2536
2 жыл бұрын
one last ride, eigenchris its been an honor
@MissPiggyM976
Жыл бұрын
Simply the best !
@greenguo1424
6 ай бұрын
13:52, sorry Christ, but how can be understand/define the r constant of motion as energy per unit mass? Thanks.
@greenguo1424
5 ай бұрын
oh okay, the immediate next slide explained. Sorry for my obtusion
@azeds
2 жыл бұрын
Keep up king
@leon_noel1687
2 жыл бұрын
And by the way, if you like to learn Quantum Field Theory, I highly recommend the very intuitive book from Jakob Schwichtenberg: No Nonsense Quantum Field Theory
@jensphiliphohmann1876
Жыл бұрын
06:00 f: _The basis vectors for the coordinates r and φ are just the partial derivatives of the position vector R› with respect to r and φ respectively._ This leads to e›_φ having length r which is o.k. for a basis vector. However, the 'e' in e›_… is actually derived from the German word "Einheitsvektor" - _unit vector_ - which implies that all those vectors should be unit vector. If so, it should be dR›/rdφ along any arc with constant r.
@luudest
Жыл бұрын
35:25 Is there a physical explantation for the perihelion shift? What causes the extra perihelion shift?
@eigenchris
Жыл бұрын
I'm not aware of any straightforward explanation, other than digging into the math of schwarzschild geodesics, and seeing that the orbits are not closed loops.
@luudest
Жыл бұрын
@@eigenchris I see, thanks
@thenimbo2
2 жыл бұрын
Newtonian gravity does predict gravitational lensing but it's half the gr value. Some dude proposed black holes in the 1700s.
@tonibat59
2 жыл бұрын
Very nice complete derivation! You might perhaps discuss how a 1/R^n grav field with n
@domenicobianchi8
7 ай бұрын
i didnt get the last part, the effect from the other planets you mentioned of 5557 is what? the advancement of the perielium due to newtonian force from the other planets?
@adixo1851
2 жыл бұрын
😗😗🔥🔥, I started watching your videos when I was in highschool, and now thanks to you I can love maths and physics. 💫💫
@lucasf.v.n.4197
Жыл бұрын
terrific; always wondered how the mercury orbit was predicted by gr;
@ankurdutta8000
Жыл бұрын
Sir can you please provide mathematica coads for plot this graph
@ShadowZZZ
2 жыл бұрын
Wow, it's insane how the predictions from GR were verified by experiments many times. Reason is absurdly Powerful
@jensphiliphohmann1876
Жыл бұрын
I must rewatch this video several times in order to understand ISCO.
@DmAlmazov
2 жыл бұрын
Penrose diagrams next video?
@eigenchris
2 жыл бұрын
Yeah, those will be in 108d. I may switch to talking about gravitational waves since I have slides ready for that and come back to 108d later.
@nandaballabhpant9557
2 жыл бұрын
It's amazing ! I have never heard in the popular science literature about the photon sphere which is 3/2 of Schwarzschild radius. On the contrary calculation based on the Newtonian gravity leads mc^2 / r = GMm/ r^2 or, r = GM/c^2 which is half of the Schwarzschild radius ( here m is mass of photon, c is the velocity of light in the vacuum, and M is the mass of the black hole)
@beagle1008
2 жыл бұрын
Thanks, Chris ,for another epic video. I take copious notes / diagrams by hand .Each 5 min of each video takes about 2 hours of work , so I fully appreciate the effort that you go to .Many thanks again.
@himanshuchaudhary5796
2 жыл бұрын
Which is the best Book to start General Relativity
@quantumofspace1367
2 жыл бұрын
Форма объёма, квантов гравитационных волн, в основном должна периодически переходить, из вход - сфера симметрично, в выход - «яйцо курицы» не симметрично, только направленно, через период нарушая симметрию - может возникнуть гравитационное притяжение тел. Но у Эйнштейна, почему-то симметрично изменяется, форма объёма гравитационной волны, и как при такой правильной симметрии, работает гравитационное притяжение тел???
@davidrandell2224
2 жыл бұрын
You- and 7 billion other brains- don’t know up from down. Down gravity: Newton, LeSage, Einstein etc. effects with no cause. Up gravity: McCutcheon expanding earth approaching the released object. D=1/2st^2 ; Galilean relative motion. All have missed this so basic fact.
@brichman8919
2 жыл бұрын
Would you be able to derive the Kerr Metric?
@eigenchris
2 жыл бұрын
I'll make an attempt in 2022, but I haven't investigated it much yet, so I can't make any guarantees.
@brichman8919
2 жыл бұрын
@@eigenchris thank you! I really enjoy your videos and learn a lot from them! Continue the great work eigenchris!
@sbkarajan
2 жыл бұрын
At 34:43, GR calculates EXACTLY 43 arcsec/century, "PERFECTLY" filling the difference between the observation and newtonian prediction using multi body solution?
@eigenchris
2 жыл бұрын
Well, nothing in physics is going to be exact. You can always ask for more decimal places or observe over longer periods of time. But the perihelion advance of Mercury had been known about for decades prior to GR. French mathematician Urbain Le Verrier calculated the error of 43 arcsec/century number in the 1850s. He originally tried to explain this by a hypothetical planet inside the orbit of Mercury that he called "Vulcan", but this didn't work out. The fact that GR calculates this 43 arcsec/century is good evidence that it explains gravity properly. (Again, the number will never be exact, but the percentage error leftover after including GR is going to be very small.) You might be interested in this wikipedia article: en.wikipedia.org/wiki/Vulcan_(hypothetical_planet)
@agnaldojunior5538
Жыл бұрын
these videos are so amazing!!!
@herwig160265
Жыл бұрын
Hi Chis, around 36:00: is there a way to see why d(ct)/dλ(1-r_s/r) is a constant of motion? I mean other than claiming it and then prove it? And also: How can you see that it is Energy per unit mass? Thanks for clarifying...
@eigenchris
Жыл бұрын
There is an alternate way of finding constants of motion using Killinf vectors, but I never learned those well enough to understand how. If you take the limit as r goes to infinity, you get E/m using E=mc^2 although I think I missed a factor of "c".
@cinemaclips4497
2 жыл бұрын
At 30:10, it seems you make mistake on substtuting r = 1/u on the (du/dΦ)^2 term. I also have a question. At 7:30, when I do the cross product of er and eΦ using the cross product formula AxB = ||A|| ||B||sinΘ, I get r since the length of er is 1 and the length of eΦ is r. But where does the ez come from?
@eigenchris
2 жыл бұрын
I'm assuming ez comes from the standard z-coordinate in cylindrical coordinates, and has a length of 1.
@abrahamalebachew4133
2 жыл бұрын
Hi Chris. Thank you for these amazing lectures on general relativity. @25:25 what do we mean by the speed of light approaching infinity? The speed of light is a constant number.
@eigenchris
2 жыл бұрын
It's sometimes the case the we can take general/special relativity and recover newtoanian physics by making the speed of light approach infinity. For example, with Lorentz transformations (written in terms of t=... instead of ct=...), if we take the limit as c goes to infinity, we get galileans transformations.
@kunx5387
Жыл бұрын
Hi eigenchris, have you discussed killing vectors related to symmetry in t, and phi elsewhere? I'm having trouble in visualizing these killing vector fields and how the quantities related to t and phi are conserved.
@eigenchris
Жыл бұрын
I don't have a video on Killing vectors, but Alex Flournoy's channel does. My understanding is that "sliding along" a Killing vector field will transform the space in a way where everything looks the same (e.g. rotating a cylinder about its axis would have a corresponding killing vector field, but turning it end-over-end would not). I think the killing vectors in the Schwrazschild case end up being the "e_t" and "e_phi" vectors, which indicate schwarzschild spacetime looks the exact same when you translate it time, or rotate along phi. This is why there are conserved quantities associated with the "t" and "phi" variables.
@cinemaclips4497
2 жыл бұрын
Will you do a playlist on quantum mechanics? Do you know of any KZitem channels that teach quantum mechanics the same way you teach relativity?
@eigenchris
2 жыл бұрын
Probably not. I don't understand QM very well. My channel has a video called "eigenchris's top math/physics youtube channels" that has a bunch of recommendation links in the description. Some are by professors and some are just random people making lectures.
@longsarith8106
2 жыл бұрын
teacher! i don't understand at point(13.56) Energy per unit mass, i think it's momentum per unit mass.
@eigenchris
2 жыл бұрын
I think to be technically correct, I needed to divide by another factor of "c" there.
@MiladParvini88
2 жыл бұрын
Your teaching is so clear, excellent, and splendid. Could you please teach Feynman integral path and Feynman diagrams like that?
@eigenchris
2 жыл бұрын
Thanks. Unfortunately I can't, because I don't understand QFT. I don't think I'll understand it anytime soon, either. You'll have to look elsewhere on KZitem.
@giovannisilvadesouza6968
2 жыл бұрын
Please at the time 19:27, you are using unit of the international system of measurements. Why the term E²/m and not E²/mc²? Because E²/m doesn't have an energy dimension, or, E really doesn't have an energy dimension!? If you answer the questions I would be very grateful, I loved your work.
@spogel9981
Жыл бұрын
I also think, that he missen the c2 anyhow before, but can not figure out where. 😒Any help out there?
@vampireegg
2 жыл бұрын
Hey eigenchris, take love. I've a question: why don't we use ict (i for imaginary) instead of ct when we take the time component in the second term (i.e, dx0/d lambda) of the geodesic equation?
@eigenchris
2 жыл бұрын
It's possible to use ict as the time coordinate, but we would have to multiply the e_t basis vector by "-i" to compensate. In my opinion having the extra factors of "i" just makes things more confusing. (Especially in the next video 108d, where the metric has off-diagonal terms... we would need to include a factor of "i" in these.) I think it's easier just to stick to real numbers.
@warrenchu6319
Жыл бұрын
27:52 How do photons have values of curly L - angular momentum per mass - since they are massless?
@eigenchris
Жыл бұрын
The analogy of "angular momentum per mass" works for massive particles because we can compare it to Newtonian equations, but the analogy won't work for massless particles. I'm not sure how to interpret "curly L", other than saying it's an abstract conserved quantity related to the phi coordinate. I'm also wondering now, looking at this video a year after making it, if there's even a possible choice for "curly L" for a light beam, or if it needs to be a fixed value.
@DiegoSilva-kk8mv
2 жыл бұрын
Thanks for the weekend gift
@NoNameAtAll2
2 жыл бұрын
4:21 is it possible for geodesic to "sometimes" have light-like tangents? i.e. not always and not never
@eigenchris
2 жыл бұрын
No, you have to pick one or the other. Massive particles never travel at the speed of light, and massless particles always travel at the speed of light.
@herwig160265
Жыл бұрын
Why is the sin term at 32:32 the reason for the perihelion advance? How do you see that? Is it because we find later, that the period is not 2 Pi?
@eigenchris
Жыл бұрын
The fact that it is multiplied by "phi" will change the period so that the orbit does not return to itself every 2pi radians.
@mehranshafieecheyki156
2 жыл бұрын
Hello christ Thank u for the vids, when will u upload new one ?
@eigenchris
2 жыл бұрын
Hi. The next video on gravitational waves has been sitting at 90% done for a while... I've just been in a bit of a rut when it comes to being productive. Should be out before the end f January.
@longsarith8106
2 жыл бұрын
Amazing video
@imaginingPhysics
2 жыл бұрын
23:55 Does this "shallow valley" correspond approximately to the normal "newtonian valley" 21:00? I guess it does. Our choice of scale just emphasizes the 1/r^3 term.
@eigenchris
2 жыл бұрын
They basically line up. You can see at 25:20 how that the location of the circular orbit in Einstein gravity (the minimum of the "potential dip") is slightly displaced by the term "12*(GM/c)^2 * L^2" under the square root. (GM/c)^2 is a very small quantity, so the shift in the "potential dip" is pretty small.
@imaginingPhysics
2 жыл бұрын
@@eigenchris Indeed the orbit corresponding to plus sign is close to Newtonian orbits. And the orbit corresponding to minus is very close to r zero.
@imaginingPhysics
2 жыл бұрын
Just a side note. 16:28 it is interesting that we do not use the geodesic equation for r component but instead make use of the constancy of magnitude of 4 velocity.
@prbmax
2 жыл бұрын
Have you ever watched YT "gavinwince?"
@eigenchris
2 жыл бұрын
Never heard of them.
@CallOFDutyMVP666
2 жыл бұрын
Awesome as Usual! S tier
@thomasmiller3957
2 жыл бұрын
Hey Eigen Chris! Your videos are great! I would like to see how to derive the de Sitter circular orbital equation (from Rindler, W. Essential Relativity (Springer-Verlag, New York, NY, 1977) p. 184): v^2 = (M/r - lambda r^2 / 3) (1 - 3M/r)^-1 Is it possible that the de Sitter solution could solve the dark matter problem? Merry Christmas! Tom-
@thomasmiller3957
2 жыл бұрын
Obviously with a negative lambda.
@eigenchris
2 жыл бұрын
Sorry but this isn't something I'm familiar with. Maybe after I finish the 110 videos (cosmology) I can ask for additional topics from GR that people want me to cover.
@souvik9305
2 жыл бұрын
In 6:21 , shouldnt the velocity in polar coordinate be dR/dt=dr/dtdR/dr+rd(phi)/dtdR/d(phi), i mean shouldnt there be an extra r in r.h.s 2nd term? I have searched in google 'velocity formula in polar cordinates' and i saw theres an extra r the R h.s in your 2nd term
@eigenchris
2 жыл бұрын
The convention I used in my videos is to NOT normalize the ϕ basis vector. You can see at 6:00 that the ϕ basis vector gets longer and longer the further we are from the origin. So the factor of "r" you mention is already included in the basis vector. This lines up with the definition "dR/dϕ = e_ϕ", since tangent vectors along ϕ-curves will get longer further from the origin, because one degree of ϕ is worth more distance further from the origin.
@souvik9305
2 жыл бұрын
Thank you so much,your videos are so amazing
@BruceWayne-qj3nv
Жыл бұрын
I’ve recently come across your videos and I have to say your videos are more detail than majority of the university lectures, and for that thank you. But one thing that bugs me about the schwarzchild metric is that when we were solving the Ricci tensors, we assumed that we were in vacuum and energy tensor was zero. But if our r=0 then for the vacuum solution the hold up, should our spherically symmetric object be a point-like mass where energy density becomes infinite? I would be more than glad if you could answer me. Thank you for your time.
@eigenchris
Жыл бұрын
I don't think we currently have a very good understanding of what singularities are. The metric fails to describe the singularity properly, because spacetime just stops. I don't think it's an accurate description of what's going on at that point.
@BruceWayne-qj3nv
Жыл бұрын
@@eigenchris Oh, I see. Physics still has a very long way to go. Again, thank you for answering me.
@it6647
2 жыл бұрын
At 31:31, w_0=1+ecos(phi) but at 33:50, it becomes 1-ecos(phi), why is that?
@eigenchris
2 жыл бұрын
I'm not sure... it might be a mistake. I'll have to take a closer look at this again and get back to you.
@eigenchris
2 жыл бұрын
I think the minus signs at 33:50 are just a mistake. It should be + e*cos(phi) in both cases. This doesn't affect the final result since the main thing we're doing on that slide is matching terms, not real algebra. You can see the equation of an ellipse written as a radial function of angle on wikipedia: en.wikipedia.org/wiki/Ellipse#Polar_form_relative_to_focus I didn't realize there were two sign conventions for the ellipse equation, and it looks like I copied down the wrong one without realizing.
@biblebot3947
2 жыл бұрын
2:00 Is the acceleration given by the definition a vector? If you expand it out by the chain then product rule, you’d get what’s called a 2-jet. Is there something I’m missing?
@eigenchris
2 жыл бұрын
I'm not familiar with what a jet is. As far as I'm aware the covariant derivative of a tangent vector is just another tangent vector.
@biblebot3947
2 жыл бұрын
@@eigenchris so d/dx denotes del_d/dx instead of the standard second derivative? If I were to apply the covariant derivative and then apply that acceleration vector to a scalar function, would that be the same as applying the derivative twice?
@eigenchris
2 жыл бұрын
I agree with your first sentence. I'm not quite sure I follow your 2nd sentence. Can you write out the equations describing the math you're taking about?
@biblebot3947
2 жыл бұрын
@@eigenchris Is (del_d/dx d/dx)f=d^2 f/df^2 ? The covariant derivative takes a vector d/dx and returns another vector. Both are derivative operators. Does the new operator acting on a function return the second derivative?
@eigenchris
2 жыл бұрын
I believe they're the same. In the left expression you would end up re-writing the derivative of d/dx using a linear combination of the chrisotoffel symbols. The result appears to be a linear combination of 1st derivative operators with coefficients in front, but it ends up being equivalent to the 2nd derivative operator on the right side of your equation. In a 2018 video on extrinsic geometry, I talk about how the christoffel symbols are basically a way of writing a 2nd derivative as a linear combination of 1st derivatives (there's an extra normal component because it's extrinsic geometry here): kzitem.info/news/bejne/knmruoKsnop7hZg
@jamsonbatista9456
Жыл бұрын
Is there a way to prove the assumption that theta is constant (pi/2)? Will be glad if you respond!
@eigenchris
Жыл бұрын
The intuitive justification is at 10:25 (we're free to choose our coordinate system so that the theta=pi/2 gives the plane of the orbit). The more mathematical justification is at 14:45 (theta=pi/2 gives a valid solution to the geodesic equation).
@jamsonbatista9456
Жыл бұрын
@@eigenchris Thank you so much
@freydrik
2 жыл бұрын
Schwartzchild’s metric is written differently in his 1916 paper, with R parameter not r. With R = (r^3+Rs^3)^(1/3)…
@eigenchris
2 жыл бұрын
I haven't read the original 1916 paper honestly. I think others found simpler derivations of the metric after he published it. The version I'm using is pretty standard in all modern GR textbooks.
@freydrik
2 жыл бұрын
@@eigenchris Thanks for your answer… I think it is OK as long as r>R (inside the metric is different) but sometimes R is Rs or sometimes it is the physical radius of the sphere; unclear to me. Also in your earlier video you make a change of variable r*sqrt(C(r)) becoming r at one point. And then C(r) is no longer mentioned afterwards. Is C(r) = 1 assumed?
@eigenchris
2 жыл бұрын
@@freydrik In 108b, you saw that the Schwarzschild "r" coordinate isn't a true radius. Instead, the "r" coordinate measures the circumference of a circle around the origin, divided by 2*pi. The scaling factor C(r) converts the radius-type-"r" to this circumference-over-2pi-type-"r". I'm not clear on your first comment... is "R" the physical radius of the body?
@jigold22571
2 жыл бұрын
🌈🔥🌈🕊❣🔥🙏
@aneikei
2 жыл бұрын
Hi, I love you're series please keep it up. That being said I have a question. @14:54 where does the "2" come from in the second geodesic equation?
@eigenchris
2 жыл бұрын
Thanks, glad you're enjoying them. The 2 comes from the fact that the θrθ and θθr coefficients are equal (because you can swap the lower indices), so rather than write out two separate terms, I just wrote out a single term with a 2 in front.
@aneikei
2 жыл бұрын
@@eigenchris Thanks, then could you also add a 2 in front of the rtt coefficient as the time indices are equal - thus can they also be swapped around? Of course I know that means they would stay the same but if the rule is that you add a 2 when the coefficients are the same and can be swapped then can that rule also be applied here as well - if not why?
@eigenchris
2 жыл бұрын
@@aneikei In the summation over μ, and ν, we can get μ=r,v=θ and then μ=θ,v=r. But there's only one way to get two t's, which is μ=t,v=t. You can imaging a 4x4 matrix where tt, rr, θθ, φφ are along the diagonal, but rθ and θr are off-diagonal mirror images of each other, so there are 2 of them overall.
@aneikei
2 жыл бұрын
@@eigenchris I understand. Thank you. Then I have one last question. Is there anyway to remove the 1/2 term from within the rtt coefficient within the geodesic equation?
@eigenchris
2 жыл бұрын
@@aneikei The 1/2 is important. If we sub in the value of rs = 2GM/c^2, (and assume r >> rs) we end up getting the classical Newtonian gravitational field of GM/r^2 (with a factor of c^2). So the 1/2 needs to be there to cancel with the 2.
@thecoloroctet1365
2 жыл бұрын
That’s all well and good, but What is Momentum??
@narfwhals7843
2 жыл бұрын
An invention of the devil to confuse humankind.
@allykid4720
2 жыл бұрын
34:35. You've mentioned perihelion shift in reality is 5600 arcsec/century, and that gravity of planets in solar system contributes 5557 of it. Could it be that remaining 43 also comes from other (undiscovered yet/discovered much later) planets and bodies like Eris, Haumea, Makemake discovered only in 2004-2005?
@narfwhals7843
2 жыл бұрын
That was the original idea. People spent a lot of time looking for "vulcan" near the sun and never found it. The object perturbing mercury would have to be restricted to a fairly small region (it would have to orbit inside mercury's orbit) to only affect it in this particular manner so it is very unlikely to be something we have just overlooked so far. Plus General Relativity explains it perfectly and is extremely well tested in other regards. It is very safe to say that this is the cause.
@allykid4720
2 жыл бұрын
@@narfwhals7843 But now your statement: "The object perturbing mercury would have be restricted to a fairly small region (it would have to orbit INSIDE mercury's orbit), so it's very unlikely to be something we have overlooked so far" contradicts with Eigenchris's statement: "5557 arcsec/century is explained by other planets' gravity", since other planets are revolving OUTSIDE of Mercury's orbit, doesn't it? -------- And it doesn't need to be something very close to Mercury. If you can explain 5557/5600 by the effects of known 8-9 distant planets of solar system, why can't other bodies in solar system explain the remaining 43/5600?
@narfwhals7843
2 жыл бұрын
@@allykid4720 We'd see the effects of objects further out on other objects as well. The other planets all affect each other, that is how we found neptune, and their effects are accounted for. The thing perturbing mercury would have to affect _only_ mercury, which basically means it must be small and close by.
@allykid4720
2 жыл бұрын
@@narfwhals7843 So, you're saying that Eigenchris's fact about other planets' influence is wrong and they don't affect Mercury's perihelion?
@narfwhals7843
2 жыл бұрын
@@allykid4720 no. I'm saying that the influence of objects outside of Mercury's orbit, like other planets, is accounted for and we would notice if there were others by their effects on the rest of the solar system. So the effect that is unaccounted for must either come from a close by object or be explained some other way.
@thespiciestmeatball
2 жыл бұрын
This was amazing. I loved seeing GR making contact with physics I’m familiar with and not being just abstract tensor calculus.
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